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| HAL : hal-00421742, version 2 |
| DOI : 10.1016/j.jfa.2009.10.011 |
| Fiche détaillée |  Récupérer au format |
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| Journal of Functional Analysis 258 (2010) 2739–2778 |
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| Versions disponibles : | v1 (03-10-2009) | v2 (04-12-2009) |
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| Spectral inequalities for non-selfadjoint elliptic operators and application to the null-controllability of parabolic systems |
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| Matthieu Léautaud 1 |
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| (02/2010) |
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| We consider elliptic operators $A$ on a bounded domain, that are compact perturbations of a selfadjoint operator. We first recall some spectral properties of such operators: localization of the spectrum and resolvent estimates. We then derive a spectral inequality that measures the norm of finite sums of root vectors of $A$ through an observation, with an exponential cost. Following the strategy of G. Lebeau and L. Robbiano (1995), we deduce the construction of a control for the non-selfadjoint parabolic problem $\partial_t u + A u = B g$. In particular, the $L^2$ norm of the control that achieves the extinction of the lower modes of $A$ is estimated. Examples and applications are provided for systems of weakly coupled parabolic equations and for the measurement of the level sets of finite sums of root functions of $A$. |
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| 1 : | Laboratoire Jacques-Louis Lions (LJLL) |
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CNRS : UMR7598 – Université Paris VI - Pierre et Marie Curie |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| Non-selfadjoint elliptic operators – Spectral theory – Coupled parabolic systems – Controllability |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00421742, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00421742 | |
| oai:hal.archives-ouvertes.fr:hal-00421742 | |
| Contributeur : Matthieu Léautaud | |
| Soumis le : Vendredi 4 Décembre 2009, 09:48:41 | |
| Dernière modification le : Mercredi 31 Mars 2010, 13:45:21 | |
